I am verifying the 6-selfridge "quadratic composite tests" detailed in my paper in the file section of this group.
I made some changes and I am now testing both the "a-1 && a+1" and "a-2 && a+2" versions in parallel. I made some speed ups in the verification program, most notably eliminating the native "%" (mod) operator where possible. I am also including testing of multiples of 7.
The paper needs to be re-published to clear up a few typos, but I am waiting for a higher limit of verification to be achieved first. I would also like to make mention of "The Cayley Hamilton Theorem" for matrices. How do I reference this?
The only thing I have noticed is that for the "a-1 && a+1" version, the gcds I find are all 1 (mod 6) and where required are for numbers, n, all 5 (mod 6).
I have my fingers in a few pies at present, but I hope to do a great deal of verification testing of these conjectures in the near future!